French and Russian Master Paintings 1870-1925 from Moscow and St PetersburgRoyal Academy, London W1; until 18 Apr

Kasimir Malevich painted his revolutionary Red Square in 1915. It remains a picture without precedent. There was Abstraction before it, but nothing as radical as this dazzling form - more of a parallelogram, in fact - its scarlet edges vibrating against a white ground, advancing like a brave new spirit.

A figure as much as a form? Indubitably. Malevich, one of 14 children born to a Ukrainian worker, subtitled it 'Painterly Realism of a Peasant Woman in Two Dimensions'. And although his subtitles are nearly as hard to fathom as his euphorically apocalyptic manifestos, you cannot misinterpret the visual language of this figure tilting through space or the life force brimming through Red Square

Ten years later, the Reds suppressed Malevich. After the revolution, it became a crime to exhibit Abstract painting. He was forced back to figuration, purged by Stalin and, 20 years later, died destitute. But his picture is irrepressible, incomparable. Nothing can put out its fire.

For proof, go if you can to the extraordinary gathering of images drawn from Russia's state museums now at the Royal Academy. Everyone knows that this was almost a no-show, that the government passed legislation to protect the art from possible seizure by restitution claimants. Anyone interested in art probably knows it's essentially a standoff between the French and Russian avant-garde. But the version of modern painting revealed here is still full of surprises as the Russians gradually release some of the missing masterpieces of 20th-century art.

Gertrude Stein liked to quip that America was the oldest country in the world because it entered the 20th century first. But she couldn't be more wrong from the perspective of art. America limps in pathetically late compared with both France and Russia. Matisse is a Fauve by 1905, Picasso paints Les Demoiselles d'Avignon two years later. Kandinsky dates - or backdates - his tendentiously titled First Abstract Painting 1910. Malevich's blazingly minimal Suprematism still looks as though it burst out of nowhere in 1913.

The crisscrossings between the two countries are continuous and astoundingly fast and can be mimicked by visitors to this show. Look at the gravely beautiful Monet Haystack in the first room and then go to Kandinsky in the last: this was what made the Russian quit law for painting. The Frenchman Carolus-Duran is palpably influenced by the flamboyant Ilya Repin, whose portrait of a barefoot Tolstoy looks remarkably like Rasputin as Santa Claus. Picasso's massive Farm Woman, her mouthless mug hacked out of wood, mute as a totem, speaks to Natalia Goncharov's monumental peasants three years later.

The Russians went west - Tatlin visited Picasso, Alexandra Exter worked with Leger, Chagall settled in Paris - giving new protein to French painting. And with the arrival of Diaghilev, Leon Bakst and the Ballets Russes, the city went wild for Russia. Simultaneously, the French started to go east, literally in the case of Matisse who was stunned by the candlelit icons in Orthodox churches. And those two great collectors, the rouble zillionaires Sergei Shchukin and Ivan Morozov, shuttled back and forth between Moscow and Paris bringing home the most advanced French art of the early 20th century.

'Shchukin,' said Daniel Kahnweiler, dealer of dealers, 'was almost the only important collector of avant-garde art.' And so it seems from this exhibition: not only had he acquired 37 Matisses, including La Danse and The Red Room, but reams of van Goghs, Cézannes, Gauguins and 50 Picassos by 1909 when he opened his palace on Sundays to the public. 'If a picture gives you a psychological shock, buy it,' he advised. 'It's a good one.' How wildly unorthodox he was can be construed from a photograph showing the Gauguins among ormolu clocks and imperial furnishings. Go from that interior to the original pictures - a super-fertile scene, say, of glowing guavas, raspberry rivers and peach-breasted girls, the paint laid down with leaden deliberation as if Gauguin were trying to keep himself under control - you may imagine why Shchukin's wife was not the only Muscovite scandalised by his collection.

La Danse, never seen in Britain before, is puffed as the main draw of this show. It turns out to be the Mona Lisa of modern art -celebrated, yet unlovable. The eye stalls over and again, tripped by the wrangled limbs of those vast, brick-red figures and it seems to me infinitely less captivating than a magnificent work like The Red Room. With its absorbed and absorbing dreamer harmoniously contained by her milieu - and his art - this is deepest Matisse: radiant, daring and full.

But the French can take care of themselves. The revelations here are nearly all Russian - not the samovars and onion domes, though even these are eccentric variants on the apples and guitars of French Modernism; and not just comparatively unknown names such as Pyotr Miturich, decoupling colour and line as gracefully as RB Kitaj 60 years in advance; but the unseen works by the heroes of Russian painting.

Isaac Levitan, Chekhov's favourite artist: it would be hard to think of a more beautiful image of late afternoon light turning field to fire than his Summer Evening 1900. Or Tatlin, whose Fish Seller, haloed by his own catch, still seems to be arriving on the canvas in a vortex of arcs and dabs. Or Chagall's much-reproduced Promenade, in which the man on the ground pulls his lover into the air like a kite, her legs dancing free in the breeze.

Russian museums have been sending pictures out to earn their living for a few years now - Picassos and Rembrandts in exchange for money to repair the rooms where they hang. Obviously the bigger the names the greater the funds, but still you can't help wishing that From Russia was weighted far more to the Russians. Then it would have been possible to show as never before in the UK the point at which Russian art takes off from France in a trail of blazing images. From Ivor Grabar's Post-Impressionist snowdrift to Malevich's Red Square is a 10-year sprint for Russia that takes France, never mind America, about another half century.

In 1935, when Malevich died, two of his canvases were smuggled into America in an umbrella. But much of the most advanced art in this show was buried by communism and lost to the public - in Russia as elsewhere - for decades. State suppression of the avant-garde didn't just halt an aesthetic revolution, it distorted the history of modern art.

Vox pop:

David Culver71, retired

Terrific. It was worth all the diplomatic drama, although I see the Russian point of view. My wife was most interested in the development of the Russian art as a result of the French influence, whereas I like the French work.

Elizabeth Maycock62, retired

It's amazing to see so many great works in such a confined space. I saw La Danse in St Petersburg. I used to teach modern dance so I'm particularly fond of it. The portrait of the bride and groom being blessed was particularly striking.

Alistair Dow36, sales administrator

A great show. I loved it. My favourite piece was the portrait of Anna Akhmatova by Natan Altman. It showed a great twist between the Russian and French work. And the Gauguins and Picassos were lovely. A coup for Norman Rosenthal.

Allison Gaynor50, mother

I'd read Hilary Spurling's books on Matisse, so I was excited to see The Red Room and La Danse. It was good to see so many female Russian artists and sad to think that the revolution stopped all that.

Eva Began61, therapist

It's amazing how much life there is in La Danse. The conceit of the big French pieces with the Russian art it inspired worked very well. The exhibition had a really good flow to it, but the Renoirs were atrocious.